### Solving Quadratic Equations by FactoringThis tutorial will guide you through the steps to solve a quadratic equation by factoring. Below is an example problem and its solution process.**Example Problem:**Solve the quadratic equation by factoring:\[ x^2 - 8x - 63 = -10x \]To solve this equation, follow these steps:1. **Move All Terms to One Side**: Start by combining like terms to set the equation equal to zero: \[ x^2 - 8x - 63 + 10x = 0 \] Simplify the equation: \[ x^2 + 2x - 63 = 0 \]2. **Factor the Quadratic Expression**: The quadratic expression $ x^2 + 2x - 63 $ needs to be factored. We need to find two numbers that multiply to -63 and add to 2. These numbers are 9 and -7. Write the expression as: \[ (x + 9)(x - 7) = 0 \]3. **Set Each Factor Equal to Zero**: Set each factor equal to zero and solve for x: \[ x + 9 = 0 \quad \Rightarrow \quad x = -9 \] \[ x - 7 = 0 \quad \Rightarrow \quad x = 7 \]Therefore, the solutions to the quadratic equation $ x^2 + 2x - 63 = 0 $ are:\[ x = -9 \quad \text{or} \quad x = 7 \]Once you've worked through the solution, enter your answer in the space provided and submit it to check your result.**Answer:**\[ x = \boxed{} \][Submit Answer]By following these steps, you can solve any quadratic equation by factoring. Practice with additional problems to master this fundamental algebra skill. ## Solving Quadratics by Factoring: Step-by-Step ExampleTo solve the quadratic equation by factoring, follow this step-by-step guide.### Step 1: Set the quadratic expression to zeroStart with your quadratic equation. For this example we have:\[ x^2 + 14x - 25 = 10x - 4 \]First, move all the terms to one side to set the equation to zero:\[ x^2 + 14x - 25 - 10x + 4 = 0 \]Simplify the expression:\[ x^2 + 4x - 21 = 0 \]### Step 2: Factor the quadratic equationNext, factor the quadratic expression. For this example, the quadratic expression $ x^2 + 4x - 21 $ factors into:\[ (x + 7)(x - 3) = 0 \]### Step 3: Set each factor to zero and solveAfter factoring the equation, set each factor equal to zero to solve for $ x $:\[ x + 7 = 0 \quad \text{or} \quad x - 3 = 0 \]Then, solve each equation:1. For $ x + 7 = 0 $:\[ x = -7 \]2. For $ x - 3 = 0 $:\[ x = 3 \]### SolutionThe solutions to the quadratic equation $ x^2 + 4x - 21 = 0 $ are:\[ x = -7 \quad \text{or} \quad x = 3 \]This step-by-step example illustrates how to solve a quadratic equation by factoring, setting each factor to zero, and solving for $ x $.

Given: To Find: To solve the given quadratic equation by factoring.

Answered: Solve the quadratic by factoring. 8х -…

Math

Algebra

Solve the quadratic by factoring. 8х - 63 -10x |

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Solve using the square root principle. Simplify completely 4(x-6)^2-35=14

A: The given equation is: 4(x-6)^2-35=14 4(x-6)^2=35+14 4(x-6)^2=49 2(x-6)=7 ( to take the positive…

Q: 16x2-256x+16=0 find the roots.

Q: )Solve the equation x2- 12x+18 0 by completing the square. Be sure to simplify all radicals. You…

Q: Find the roots of x+2x+5=0 by using quadratic formula.

Q: Write the quadratic equation in 1. 10 21)

Q: 1.Determine and state the most efficient way of solving the quadratic equation. Then solve the…

A: Topic- Quadratic Equation

Q: 10. x2 - 14x + c 12. x2 + 5x + c 14. x2 - x + c

A: 10) the complete square will be (x-7)^2 12) the complete square will be (x+5/2)^2

Q: 8. y -8 -6 -4 -2 Answers: N. 4, 2.

Q: Value of a b and c in quadratic equation 2xsquared-7x-9=0

A: The standard form is given by: Where a, b, and c are constants, or numerical coefficients, and x is…

Q: the Solve for by using completing square 2x- 3x -1 =0

A: we have to solve for x by using completing the square 2x2-3x-1=0

Q: Solve for the roots 3x2-5x+2

A: Solution :-

Q: solve a. 2x2 + 9x + 7 = 3

A: Consider the quadratic equation, 2x2+9x+7=3 Subtract “3” from both sides, 2x2+9x+7-3=3-32x2+9x+4=0…

Q: Use the technique of completing the square to transform the quadratic equation into the form…

Question

### Solving Quadratic Equations by Factoring

This tutorial will guide you through the steps to solve a quadratic equation by factoring. Below is an example problem and its solution process.

**Example Problem:**

Solve the quadratic equation by factoring:

\[ x^2 - 8x - 63 = -10x \]

To solve this equation, follow these steps:

1. **Move All Terms to One Side**:
Start by combining like terms to set the equation equal to zero:
\[ x^2 - 8x - 63 + 10x = 0 \]
Simplify the equation:
\[ x^2 + 2x - 63 = 0 \]

2. **Factor the Quadratic Expression**:
The quadratic expression $ x^2 + 2x - 63 $ needs to be factored. We need to find two numbers that multiply to -63 and add to 2. These numbers are 9 and -7.
Write the expression as:
\[ (x + 9)(x - 7) = 0 \]

3. **Set Each Factor Equal to Zero**:
Set each factor equal to zero and solve for x:
\[ x + 9 = 0 \quad \Rightarrow \quad x = -9 \]
\[ x - 7 = 0 \quad \Rightarrow \quad x = 7 \]

Therefore, the solutions to the quadratic equation $ x^2 + 2x - 63 = 0 $ are:

\[ x = -9 \quad \text{or} \quad x = 7 \]

Once you've worked through the solution, enter your answer in the space provided and submit it to check your result.

**Answer:**
\[ x = \boxed{} \]

[Submit Answer]

By following these steps, you can solve any quadratic equation by factoring. Practice with additional problems to master this fundamental algebra skill.

## Solving Quadratics by Factoring: Step-by-Step Example

To solve the quadratic equation by factoring, follow this step-by-step guide.

### Step 1: Set the quadratic expression to zero

Start with your quadratic equation. For this example we have:

\[ x^2 + 14x - 25 = 10x - 4 \]

First, move all the terms to one side to set the equation to zero:

\[ x^2 + 14x - 25 - 10x + 4 = 0 \]

Simplify the expression:

\[ x^2 + 4x - 21 = 0 \]

### Step 2: Factor the quadratic equation

Next, factor the quadratic expression. For this example, the quadratic expression $ x^2 + 4x - 21 $ factors into:

\[ (x + 7)(x - 3) = 0 \]

### Step 3: Set each factor to zero and solve

After factoring the equation, set each factor equal to zero to solve for $ x $:

\[ x + 7 = 0 \quad \text{or} \quad x - 3 = 0 \]

Then, solve each equation:

1. For $ x + 7 = 0 $:

\[ x = -7 \]

2. For $ x - 3 = 0 $:

\[ x = 3 \]

### Solution

The solutions to the quadratic equation $ x^2 + 4x - 21 = 0 $ are:

\[ x = -7 \quad \text{or} \quad x = 3 \]

This step-by-step example illustrates how to solve a quadratic equation by factoring, setting each factor to zero, and solving for $ x $.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Quadratic Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Which expression represents the proper use of the quadratic formula to solve the equation x2 = 6x + 4? 6+ V36 – 16 2 6+ v36 + 16 2 - 6+ V36 + 16 2 - 6+ V36 – 16
-10 11 2. Use the quadratic formula to solve the equation 10x2-22x-17=12x+7. Verify the solutions by factoring. Show all work.
Write a quadratic equation in standard form with the given solution set. {−12, 25} (Type an equation whose terms have 1 as their greatest common factor.)
Solve quadratic equation. 9- 6x + x2 = 0